Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26030279 | C2 | semidirect |
| 3. #26025611 | C2 | semidirect |
| 4. #26018682 | C2 | semidirect |
| 5. #26018642 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1517 | C2 | semidirect |
| 93. C2×D356 | SD16 | semidirect |
| 236. #1517 | D89 | semidirect |
| 240. C89 | #9998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030279 | 2 |
| #26029712 | 2 |
| #26025611 | 2 |
| #26018682 | 2 |
| #26018642 | 2 |
| #26018110 | 2 |
| C89×#1517 | 2 |
| #9998 | 89 |